Turn up, dropping round initially for church record store (7)
I believe the answer is:
archive
'record store' is the definition.
(where records are stored)
'turn up' is the wordplay.
'turn' becomes 'arc' (I've seen this before).
'up' becomes 'hive' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'arc'+'hive'='ARCHIVE'
'dropping round initially for church' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
(Other definitions for archive that I've seen before include "Record repository" , "Record, annal" , "Document depository" , "Depository containing historical records" , "Data repository" .)